Non-toxic liquid impregnated surfaces

ABSTRACT

Embodiments described herein relate generally to containers having liquid-impregnated surfaces disposed on their interior surfaces. The liquid-impregnated surfaces may compose an arrangement of solid and/or semi-solid features, defining one or more interstitial regions therebetween, and an impregnating liquid preferentially wetted to those regions. The containers may be designed to contain a product that is intended for human or animal consumption. The solid and/or semi-solid features and the impregnating liquid collectively define a secondary surface (e.g., substantially parallel to the interior surface on which the liquid-impregnated surfaces are disposed) and may include materials which are non-toxic. In particular, non-toxic liquid-impregnated surfaces of the disclosure may be configured for use in food, drugs, health and/or beauty product applications.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.61/878,481, entitled “Non-Toxic Liquid-Impregnated Surfaces.” filed Sep.16, 2013, the disclosure of which is incorporated herein by reference inits entirety.

BACKGROUND

The advent of micro/nano-engineered surfaces in the last decade hasopened up new techniques for enhancing a wide variety of physicalphenomena in thermofluids sciences. For example, the use of micro/nanosurface textures has provided non-wetting surfaces capable of achievingless viscous drag, reduced adhesion to ice and other materials,self-cleaning, water repellency, and other useful properties. Theseimprovements result generally from diminished contact (i.e., lesswetting) between the solid surfaces, and adjacent liquids. One type ofnon-wetting surface of interest is a super hydrophobic surface. Ingeneral, a super hydrophobic surface includes micro/nano-scale roughnesson an intrinsically hydrophobic surface, such as a hydrophobic coating.Super hydrophobic surfaces resist contact with water by virtue of anair-water interface within the micro/nano surface textures.

One of the drawbacks of existing non-wetting surfaces (e.g.,superhydrophobic, superoleophobic, and supermetallophobic surfaces) isthat they are susceptible to evaporation and partial entrainment ofconstituents therein (e.g., in the presence of water and/or a product incontact with the surface), which can degrade the hydrophobicity, and ina consumer products context may lead to concerns about materialstoxicity (i.e., as they degrade and/or dissociate). Thus, there is aneed for non-wetting surfaces that are more robust. In particular, thereis a need for non-wetting surfaces that are non-toxic, are more durable,and can maintain super hydrophobicity even after repeated use.

SUMMARY

Embodiments described herein relate generally to containers havingliquid-impregnated surfaces disposed on their interior surfaces. Theliquid-impregnated surfaces may compose an arrangement of solid and/orsemi-solid features, defining one or more interstitial regionstherebetween, and an impregnating liquid preferentially wetted to thoseregions. The containers may be designed to contain a product that isintended for human or animal consumption. The solid and/or semi-solidfeatures and the impregnating liquid collectively define a secondarysurface (e.g., substantially parallel to the interior surface on whichthe liquid-impregnated surfaces are disposed) and may include materialswhich are non-toxic. In particular, non-toxic liquid-impregnatedsurfaces of the disclosure may be configured for use in food, drug,health and/or beauty product applications, and industrial applicationswhere people make contact with the coating materials, or where fumes orvapors in the manufacturing of coating materials or products made in theindustrial applications poses a safety concerns for workers.

In some embodiments, the interstitial regions are dimensioned andconfigured such that the impregnating liquid is retained within theinterstitial regions by capillary forces. The impregnating liquiddisposed in the interstitial regions and the solid features collectivelydefines a secondary surface having a second roll off angle less than afirst roll off angle of the initial/interior surface. Theliquid-impregnated surface, in use, is in contact with at least one of afood product, drug, or health and beauty product, and the impregnatingliquid included in the liquid-impregnated surface is non-toxic. In someembodiments, the solid features included in the liquid-impregnatedsurface can also be formed from materials that are non-toxic. In someembodiments, at least one of the impregnating liquid and the solidfeatures included in the liquid-impregnated surface can include:materials that are approved by the U.S. Food and Drug Administration(FDA) for use as a food additive, an FDA approved food contactsubstance, an FDA “Generally Regarded as Safe” (GRAS) material, an FDAapproved drug ingredient, and/or or an FDA approved health and beautyproduct ingredient.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic cross-section view of a product contacting aconventional super-hydrophobic surface, and FIG. 1B shows theconventional non-wetting surface after a product has impaled thesurface.

FIG. 2 shows a schematic cross-section of a liquid-impregnated surfaceaccording to an embodiment.

FIG. 3 is a scanning electron microscope (SEM) micrograph of a surfaceincluding semi-solid features according, to an embodiment.

FIG. 4 is a SEM micrograph of a surface including hierarchicalsemi-solid features, according to an embodiment.

FIG. 5 is a SEM micrograph of the surface of FIG. 3 partiallyimpregnated with an impregnating liquid.

FIG. 6 is an enlarged higher-magnification view of the region of theliquid-impregnated surface indicated by arrow A in FIG. 5.

FIGS. 7A and 7B are schematic diagrams of liquid droplets placed on aliquid-impregnated surfaces (having a low surface energy lubricant, anda having moderate surface energy lubricant, respectively) according toan embodiment.

FIGS. 7C and 7D show photographs of water droplets on theliquid-impregnated surfaces of FIGS. 7A and 7B, respectively.

FIGS. 7E and 7F are photographs of water droplets on theliquid-impregnated surfaces of FIGS. 7A and 7B, taken under afluorescent light, where the liquid includes a fluorescent dye.

FIGS. 7G and 7H are LCFM images of liquid-impregnated surfaces (having alow surface energy lubricant, and a having moderate surface energylubricant, respectively) according to an embodiment.

FIGS. 7I and 7J are environmental scanning electron microscope (ESEM)images of liquid-impregnated surfaces (having a low surface energylubricant, and a having moderate surface energy lubricant, respectively)according to an embodiment.

FIG. 8 is a table of schematics and characteristic equations for wettingsurface configurations having an oil-solid-air interface (top threerows) and at an oil-solid-water interface (bottom three rows), where thesubscript “o” denotes the impregnating liquid (e.g. oil).

FIG. 9 shows possible thermodynamic states of a water droplet (or otherexternal phase) on liquid-impregnated surfaces.

FIG. 10A is a plot of measured roll off angles for liquid-impregnatedsurfaces, according to an embodiment.

FIG. 10B is a SEM image of a liquid-impregnated surface with solidfeatures, according to an embodiment.

FIG. 10C is a SEM image of a liquid-impregnated surface havinghierarchical solid features, according to an embodiment.

FIG. 10D is a non-dimensional plot of scaled gravitational force at theinstant of roll-off, as a function of the relevant pinning force of theliquid-impregnated and non-impregnated surfaces of FIG. 9.

FIG. 11A is a plot of measured velocities of water droplets as afunction of substrate tilt angle, according to an embodiment.

FIG. 11B shows a schematic of a liquid droplet moving on alubricant-impregnated surface, showing the various parameters consideredin the scaling model, according to an embodiment.

FIG. 11C shows trajectories of a number of coffee particles measuredrelative to a water droplet on a liquid-impregnated surface, accordingto an embodiment.

FIG. 11D shows a non-dimensional plot obtained from a model describedherein.

FIG. 12 shows a SEM micrograph (at 500× magnification) of a texturedsubstrate formed by spraying a mixture of 0.5 grams carnauba wax and 40ml ethanol onto a substrate, according to an embodiment.

FIG. 13 is a higher-magnification (15,000×) SEM micrograph of thetextured substrate shown in FIG. 12.

FIG. 14 shows a scanning electron microscope (SEM) micrograph of atextured substrate formed by spraying a mixture of 4 grams carnauba waxand 40 ml ethanol onto a substrate, according to an embodiment.

FIG. 15 is a higher-magnification (15,000×) SEM micrograph of thetextured substrate shown in FIG. 14.

FIG. 16 is a SEM micrograph (at 500× magnification) of a texturedsubstrate formed by spraying an aerosol wax on a substrate, according toan embodiment.

FIG. 17 is a higher-magnification (15,000×) SEM micrograph of thetextured substrate shown in FIG. 16.

FIGS. 18-23 are a sequence of images of a volume of ketchup disposed ona liquid impregnated surface that includes aerosol wax as the solid andethyl oleate as the impregnating liquid, such that the volume of ketchupslides on the liquid impregnated surface as the liquid impregnatedsurface is inclined at an angle.

DETAILED DESCRIPTION

Embodiments described herein relate generally to containers havingliquid-impregnated surfaces disposed on their interior surfaces. Theliquid-impregnated surfaces may compose an arrangement of solid and/orsemi-solid features, defining one or more interstitial regionstherebetween, and an impregnating liquid preferentially wetted to thoseregions. The containers may be designed to contain a product that isintended for human or animal use and/or consumption. The solid and/orsemi-solid features and the impregnating liquid collectively define asecondary surface (e.g., substantially parallel to the interior surfaceon which the liquid-impregnated surfaces are disposed) and may includematerials which are non-toxic. In particular, non-toxicliquid-impregnated surfaces of the disclosure may be configured for usein food, drugs, health and/or beauty product applications.

In some embodiments, the interstitial regions are dimensioned andconfigured such that the impregnating liquid is retained within theinterstitial regions by capillary forces. The secondary surface may havea second roll off angle less than a first roll off angle of theinitial/interior surface. The liquid-impregnated surface, in use, is incontact with at least one of a food product, drug, or health and beautyproduct, and the impregnating liquid included in the liquid-impregnatedsurface is non-toxic. In some embodiments, the solid features includedin the liquid-impregnated surface can also be formed from materials thatare non-toxic. In some embodiments, at least one of the impregnatingliquid and the solid features included in the liquid-impregnated surfacecan include: materials that are approved by the U.S. Food and DrugAdministration (FDA) for use as a food additive, an FDA approved foodcontact substance, an FDA “Generally Regarded as Safe” (GRAS) material,an FDA approved drug ingredient, and/or or an FDA approved health andbeauty product ingredient.

Some surfaces with designed chemistry and roughness possess substantialnon-wetting (hydrophobic) properties, which can be extremely useful in awide variety of commercial and technological applications. Inspired bynature, such hydrophobic surfaces include air pockets trapped within amicrotexture or nanotexture of the surface which diminishes the contactangle between such hydrophobic surfaces and a liquid thereon, orexample, water, an aqueous liquid, or any other aqueous product. As longas the air pockets are stable, the surface continues to exhibithydrophobic behavior. Such hydrophobic surfaces that include airpockets, however, present certain limitations including, for example: i)the air pockets can be collapsed by external wetting pressures, ii) theair pockets can diffuse away into the surrounding liquid, iii) thesurface can lose robustness upon damage to the texture, iv) the airpockets may be displaced by low surface tension liquids unless specialtexture design is implemented, and v) condensation or frost nuclei,which can form at the nanoscale throughout the texture, can completelytransform the wetting properties and render the textured surface highlywetting.

Non-toxic liquid-impregnated surface coatings described herein includeimpregnating liquids that are impregnated into a surface that includesan arrangement or “matrix” of solid features defining one or moreinterstitial regions (i.e., between individual features and/or betweengroupings of features), such that the interstitial regions includevolumes or “pockets” of impregnating liquid. The impregnating liquid isconfigured to wet the solid surface preferentially, and it adheres tothe micro-textured surface with strong capillary forces, enabling anextremely low roll-off angle of a droplet and/or aqueous solution(referred to as contact liquid) that is in contact with the surface. Forexample, in some embodiments, the roll-off angle of the contact liquidin contact with the surface is about 1 degree. This enables the contactliquid to displace, travel, slide, roll off, etc., with substantial easeon the liquid-impregnated surface. Therefore, the non-toxicliquid-impregnated surfaces described herein, provide certainsignificant advantages over conventional super hydrophobic surfacesincluding: (i) low hysteresis, (ii) self cleaning properties, (iii)ability to withstand high drop impact pressure (i.e., are wearresistant), (iv) ability to self heal by capillary wicking upon damage;(v) ability to enhance condensation; and (vi) in the event ofevaporation and/or entrainment, toxicity is avoided due to the non-toxiccomposition of the materials employed. The non-toxic liquid-impregnatedsurfaces described herein, which may include solids and/or impregnatingliquids that are non-toxic, can be used in applications requiringcontact with a variety of products destined for human use orconsumption, such as, for example; (a) food products such as, forexample ketchup, catsup, mustard, mayonnaise, syrup, honey, jelly, etc.;(b) drugs, for example Food and Drug Administration (FDA) approveddrugs; and (c) consumer products, for example toothpaste, shampoo,conditioner, hair gel, etc. Furthermore, methods described herein, canenhance the durability of liquid-impregnated surfaces, such that thesurface does not wear, wears more slowly, and/or replenishes itselfafter single and/or repeated use. Examples of liquid-impregnatedsurfaces, methods of making liquid-impregnated surfaces, andapplications thereof, are described in U.S. Pat. No. 8,574,704 (alsoreferred to as “the '704 patent”), entitled “Liquid-ImpregnatedSurfaces, Methods of Making, and Devices Incorporating the Same,” issuedNov. 5, 2013, and International Publication Number WO2014/078867,entitled “Apparatus and Methods for Employing Liquid-ImpregnatedSurfaces,” published May 22, 2014, the contents of which are herebyincorporated herein by reference in their entirety. Examples ofmaterials used for forming the solid features on the surface,impregnating liquids, and applications involving edible contact liquids,are described in U.S. Patent Application Publication No. 2013/0251952(also referred to as “the '952 publication), entitled “Self-LubricatingSurfaces for Food Packaging and Food Processing Equipment,” publishedSep. 26, 2013, the content of which is hereby incorporated herein byreference in its entirety.

As used herein, the terms “about” and “approximately” generally meanplus or minus 10% of the value stated, for example “about 250 μm” wouldinclude any value from 225 μm to 275 μm, and “approximately 1,000 μm”(or “1 mm”) would include any value from 900 μm to 1,100 μm.

As used herein, the phrase “contact liquid” and the terms “fluid” and“product” may refer to a solid or liquid that flows, for example anon-Newtonian fluid, a Bingham fluid, or a thixotropic fluid. A “contactliquid” is any such material that is in contact with aliquid-impregnated surface, unless otherwise stated.

As used herein, “emerged area fraction” (also “non-submerged areafraction”), or “,” is defined as a representative fraction of thesurface area of a liquid-impregnated surface corresponding withnon-submerged solid (i.e., solid that is not covered up by theimpregnating liquid, and hence may be in direct contact with an adjacentproduct material) at room temperature.

Referring now to FIGS. 1A and 1B, a conventional non-wetting surface 10is a textured surface configured such that the non-wetting surface 10includes a plurality of solid features 12 disposed on the surface 10.The solid features 12 define interstitial regions between each of theplurality of solid features which are impregnated by a gas, for example,air. A product P (e.g., a non-Newtonian fluid, a Bingham fluid or athixotropic fluid) is disposed on the conventional non-wetting surfacesuch that the product contacts a top portion of the solid features at agas-product interface 14, and the interface 14 is configured such thatit prevents or delays the product from wetting the entire surface 10.Under certain conditions, the product P can displace and/or dissolve theimpregnating gas and “impales” the interstitial regions between thefeatures 12 of the surface 10 (it may also be said that the product P is“impaled” by the features). Such impalement may occur, for example, whena droplet of the product P impinges the surface 10 at a high velocity.When impalement occurs, the gas occupying the regions between the solidfeatures 12 is replaced with the product P, either partially orcompletely, and the surface 10 may lose its non-wetting capabilities asa consequence.

Referring now to FIG. 2, in some embodiments a liquid-impregnatedsurface 130 includes a solid surface 110 that includes a plurality ofsolid features 112 disposed on the solid surface 110 (e.g., the solidfeatures projecting therefrom, adhered thereon/thereto, or comprisingprojections between recessed regions in the surface, and/or the like)such that the plurality of solid features 112 define interstitialregions between each (individual) of the plurality of solid featuresand/or between clusters of such solid features. An impregnating liquid120 is “impregnated” (e.g., introduced, pumped, brushed, applied,injected, rolled, sprayed, poured, etc.) into the interstitial regionsdefined by the plurality of solid features 112. A product P is disposedon the liquid-impregnated surface 100 such that a liquid-productinterface 124 separates the product P from the surface 110 and preventsthe product P from entirely wetting the surface 110. Theliquid-impregnating surface 130 having a product disposed thereon iscollectively indicated by reference numeral 100.

The product P can be any product, for example, a non-Newtonian fluid, aBingham fluid, a thixotropic fluid, a high viscosity fluid, a high zeroshear rate viscosity fluid (shear-thinning fluid), a shear-thickeningfluid, and/or a fluid having a high surface tension. The product P caninclude, for example a food product, a drug, a health and/or beautyproduct, and/or any other product described herein, or a combinationthereof.

The surface 110 can be any surface that has a first roll off angle or noroll-off angle (e.g. a really sticky surface), for example a roll offangle of a product in contact with the surface 110 (e.g., water, foodproducts, drugs, health or beauty products, or any other productsdescribed herein) under a specified environmental condition (e.g.,temperature, pressure, etc.). The surface 110 can be a flat surface, forexample, a silicon wafer, a plastic sheet stock, a metal sheet stock, aglass wafer, a ceramic substrate, a table top, a wall, a wind shield, aski goggle screen, etc. The surface 110 can also be a contoured surface,for example a container, a propeller, a pipe, etc.

In some embodiments, the surface 110 can include an interior surface ofa container for housing the product P, and the container may be any ofthe following exemplary containers: tube, bottle, hopper, tray, vial,flask, mold, jar, cup, glass, pitcher, barrel, bin, tote, tank, keg,tub, syringe, tin, pouch, box (e.g., a lined box), hose, cylinder, andcan (e.g., a tin can). The container can be constructed in almost anydesirable shape. In some embodiments, the surface 110 can be an interiorsurface of a hose, a pipe, a conduit, a nozzle, a paint applicator(e.g., a paint sprayer), a syringe needle, a dispensing tip, a lid, apump, and/or a surface of any other apparatus for containing,transporting, and/or dispensing a product P. The surface 110, forexample comprising the interior surface of a container, can beconstructed of any suitable material, including plastic, glass, metal(including metal meshes and metallic containers lined with linen),Styrofoam, ceramic, coated fibers, and combinations thereof. Suitablesurfaces can also include, for example, polystyrene, nylon,polypropylene, wax, polyethylene terephthalate, polypropylene,polyethylene (e.g., low-density polyethylene, LDPE; high-densitypolyethylene, HDPE; polyethylene terephthalate, PET), polyurethane,polysulphone, polyethersulfone, polytetrafluoroethylene (PTFE),tetrafluoroethylene (TFE), fluorinated ethylenepropylene copolymer(FEP), polyvinylidene fluoride (PVDF),perfluoroalkoxytetrafluoroethylene copolymer (PFA), perfluoromethylvinylether copolymer (MFA), ethylenechlorotrifluoroethylene copolymer(ECTFE), ethylene-tetrafluoroethylene copolymer (ETFE),perfluoropolyether, Tecnoflon cellulose acetate, and polycarbonate. Thecontainer 110 can be constructed of rigid or flexible materials.Foil-lined and polymer-lined cardboard, corrugated, and/or paper boxescan also form suitable containers. In some embodiments, the surface canbe solid, smooth, textured, rough, and/or porous.

The solid features 112 can be disposed on the surface 110 using anysuitable method. For example, the solid features 112 can be applied tothe inside of a container (e.g., a bottle or other food container), orthey can be integral to the surface itself (e.g., the textures of apolycarbonate bottle may be made of polycarbonate). In some embodiments,the solid features 112 may be formed of a collection or coating ofparticles, for example edible solid particles. Examples of solid,non-toxic and/or edible materials include (but are not limited to):insoluble fibers (e.g., purified wood cellulose, micro-crystallinecellulose, and/or oat bran fiber), wax (e.g., carnauba wax, japan wax,beeswax, candelilla wax), pulp, zein, dextrin, cellulose, celluloseethers (e.g., Hydroxyethyl cellulose, Hydroxypropyl cellulose (HPC),Hydroxyethyl methyl cellulose, Hydroxypropyl methyl cellulose (HPMC),Ethyl hydroxyethyl cellulose), ferric oxide, iron oxide, sodium formate,sodium oleate, sodium palmitate, sodium sulfate, gelatin, pectin,gluten, starch alginate, carrageenan, whey and/or any other edible solidparticles described herein, or any combination thereof.

In some embodiments, the solid features may comprise a material having amelting point of about 75° C. In other embodiments, the solid featuresmay comprise a material having a melting point of as high as 330° C., ashigh as 240° C. (e.g., for polyurethanes), as high as 60° C., as high as50° C., between about 40° C. and about 50° C. In other embodiments, thesolid features may comprise a material having a melting point of atleast about 60° C. In still other embodiments, the solid features maycomprise a material having a melting point may be as high as about2,000° C.

In some embodiments, the solid features may comprise materials that aresafe for contact with skin, such as a silicone, fluoropolymers (e.g.,polytetrafluoroethylene, polychlorotrifluoroethylene, poly(vinylidenedifluoride)), nitrile and silicone rubbers, fluorosilicone,polyurethane, fluoropolyurethane, polyvinylpyrrolidone, fluoroacrylatesand halocarbons in general, and their corresponding copolymers withhydrocarbons, silicones, acrylates, methacrylates, urethanes and otherfluoropolymers (e.g. poly(vinylidene fluoride-o-hexafluoropropylene)).In some embodiments, the solid features may comprise particlesincluding: halocarbons (e.g., polytetrafluoroethylene, polyvinylidenefluoride, chlorotrifluoroethylene, ethylene chlorotrifluoroethylene),ceramics (e.g., surface modified), and metal oxides (e.g., surfacemodified).

In some embodiments, the solid features may comprise one or more of thefollowing substances: Japan wax, beeswax, carnauba wax, rice bran wax, amineral wax, paraffin wax, candelilla wax, zein, shellac, methylcellulose, stearic acid, cetyl alcohol, stearic alcohol, calciumstearate, zinc stearate, magnesium stearate, titanium oxide, sodiumoleate, sodium palmitate, polydimethylsiloxane (PDMS), andsilicone-based sealant, silicone wax, and silicone-based sealant. Insome embodiments, materials employed in the formulation of the solidfeatures may have a solubility in an impregnating liquid of thedisclosure of not more than 1% (w/w).

In some embodiments, the solid features 112 can be formed by exposingthe surface 110 (e.g., polycarbonate) to a solvent (e.g., acetone)(i.e., chemical roughening). For example, the solvent may impart textureby inducing crystallization (e.g., polycarbonate may recrystallize whenexposed to acetone). In some embodiments, the solid features 112 can bedisposed by dissolving, etching, melting, milling, laser rastering,oxidizing (e.g. by boiling in water) and/or evaporating away a portionof a surface, leaving behind a textured, porous, and/or rough surfacethat includes a plurality of the solid features 112. In someembodiments, the solid features 112 can be defined by mechanicalroughening (e.g., tumbling with an abrasive or sand-blasting),spray-coating, polymer spinning, deposition of particles from solution(e.g., layer-by-layer deposition, evaporating away liquid from aliquid/particle suspension), and/or extrusion or blow-molding of a foam,or foam-forming material (for example a polyurethane foam). In someembodiments, the solid features 112 can also be formed by deposition ofa polymer from a solution (e.g., the polymer forms a rough, porous, ortextured surface); extrusion or blow-molding of a material that expandsupon cooling, leaving behind a wrinkled surface; and application of alayer of a material onto a surface that is under tension or compression,and subsequently relaxing the tension or compression of surface beneath,resulting in a textured surface.

In some embodiments, the solid features 112 are formed by non-solventinduced phase separation of a polymer, resulting in a sponge-like porousstructure. For example, a solution of polysulfone,poly(vinylpyrrolidone), and dimethylacetamide (DMAc). may be cast onto asubstrate and then immersed in a bath of water. Upon immersion in water,the solvent and non-solvent exchange, and the polysulfone precipitatesand hardens.

In some embodiments, the solid features 112 may be formed by aself-assembly process, for example the co-deposition of solid andliquid. The self-assembly process may involve the use of molecules suchas: alkylthiols, alhyldisulfides, alkylselenols, organosilanes,organophosphonates, organophosphates, alkylcarboxilate, among others,for example including different terminal groups configured to modify thechemistry of the surface.

The solid features 112 can include micro-scale features such as, forexample posts, spheres, nano needles, pores, cavities, interconnectedpores, grooves, ridges, interconnected cavities, or any other randomgeometry that provides a micro and/or nano surface roughness (forexample, a roughness averaged over 5 peaks, “S5P,” of less than about 25μm, 10 μm, e.g., 3 μm), 1 μm, 500 nm. In some embodiments, the solidfeatures 112 can include particles that have micro-scale dimensions thatcan be randomly or uniformly dispersed on a surface. Characteristicspacing between the solid features 112 can be about 200 μm, about 100μm, about 90 μm, about 80 μm, about 70 μm, about 60 μm, about 50 μm,about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm, betweenabout 2 μm and about 5 μm, about 1 μm, or about 100 nm. Thecharacteristic spacing may be uniform or non-uniform (ordered changes inspacing, linearly varying spacing, random spacing, and/or the like). Insome embodiments the spacing is nonuniform provided that the spacingbetween features on over 99% of the surface does not exceed 200 μm,about 100 μm, about 90 μm, about 80 μm, about 70 μm, about 60 μm, about50 μm, about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm,between about 2 μm and about 5 μm, about 1 μm, or about 100 nm. Here 99%is only important because it means that there are few defect spots wherethere could be a larger separation between features consequent pinningof the product in those regions. In some embodiments, the characteristicspacing between the solid features 112 can be (e.g., on average) in therange of about 100 μm to about 100 nm, about 30 μm to about 1 μm, orabout 10 μm to about 1 μm. In some embodiments, characteristic spacingbetween solid features 112 can be (e.g., on average) in the range ofabout 100 μm to about 80 μm, about 80 μm to about 50 μm, about 50 μm toabout 30 μm, or about 30 μm to about 10 μm, inclusive of all rangestherebetween.

In some embodiments, the solid features 112, for example solid“particles,” can have an average dimension (e.g., corresponding to aheight, width, diameter, length, and/or the like) of about 200 μm, about100 μm, about 90 μm, about 80 μm, about 70 μm, about 60 μm, about 50 μm,about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm, about 1μm, about 0.5 μm, between 0.5 μm and 10 μm, or about 100 nm. In someembodiments, the average dimension of the solid features 112 can be in arange of about 100 μm to about 100 nm, about 30 μm to about 10 μm, orabout 20 μm to about 1 μm. In some embodiments, the average dimension ofthe solid features 112 can be in a range of about 10 nm to about 50 μm.In some embodiments, the average dimension of the solid features 112 canbe in the range of about 100 μm to about 80 μm, about 80 μm to about 50μm, about 50 μm to about 30 μm, or about 30 μm to about 10 μm, or 10 μmto 100 nm, inclusive of all ranges therebetween. In some embodiments,the height of the solid features 112 can be substantially uniform. Insome embodiments, the surface 110 can have hierarchical features, forexample micro-scale features that further include nano-scale featuresdisposed thereupon (e.g., etched therein, adhered thereto, etc.).

In some embodiments, the solid features 112 (e.g., particles) can beporous. The characteristic pore size (e.g., pore width or length) ofparticles can be (e.g., on average) about 5,000 nm, about 3,000 nm,about 2,000 nm, about 1,000 nm, about 500 nm, about 400 nm, about 300nm, about 200 nm, about 100 nm, about 80 nm, about 50, about 10 nm. Insome embodiments, the characteristic pore size can be in the range ofabout 200 nm to about 2 μm, or about 50 nm to about 1 μm, inclusive ofall ranges therebetween.

The impregnating liquid 120 is disposed on the surface 110 such that theimpregnating liquid 120 impregnates substantially all of theinterstitial regions defined by the plurality of solid features 112 (thesolid features comprising, for example, pores, cavities, or otherwiseinter-feature spacing defined by the surface 110), such that no airremains in the interstitial regions. The interstitial regions can bedimensioned and configured such that capillary forces retain part of theimpregnating liquid 120 in the interstitial regions. The impregnatingliquid 120 disposed in the interstitial regions of the plurality ofsolid features 112 is configured such that the liquid-impregnatedsurface 130 defines a second roll off angle that is less than the firstroll of angle (i.e., the roll of angle of the un-impregnated liquidsurface 110). In some embodiments, the impregnating liquid 120 can havea viscosity at room temperature of less than about 1,000 cP, for exampleabout 8 cP, between about 1 cP and about 10 cP, between about 10 cP andabout 20 cP, about 50 cP about 30 cP, between about 8 cP and about 30cP, about 50 cP, about 80 cP, between about 20 cP and about 100 cP,about 100 cP, between about 100 cP and about 10 P, about 150 cP, about200 cP, about 300 cP, about 350 cP, about 400 cP, about 500 cP, about600 cP, about 700 cP, about 800 cP, about 900 cP, between about 10 P andabout 100 P, about 1,000 cP, or between about 100 P and about 1,000 P,inclusive of all ranges therebetween. In some embodiments, theimpregnating liquid 120 can have a viscosity of about 8 cP or less. Insome embodiments, the impregnating liquid 120 can have a viscosity ofabout 1,000 cP or less. In some embodiments, the impregnating liquid 120can have a vapor pressure at room temperature of less than about 20mmHg. In some embodiments, the impregnating liquid 120 can have a vaporpressure at room temperature of as low as 4×100⁻⁷ mmHg. In someembodiments, the impregnating liquid 120 can have a surface tension ofas low as 14 dyn/cm. In some embodiments, the impregnating liquid 120can fill the interstitial regions defined by the solid features 112 andform a layer of at least about 5 nm thick above the plurality of solidfeatures 112 disposed on the surface 110. In some embodiments, theimpregnating liquid 120 forms a layer of at least about 1 μm of excessmobile liquid (easily moved by external forces such as those resultingfrom shearing or gravity) above the plurality of solid features 112disposed on the surface 110 on some regions of the surface.

The impregnating liquid 120 may be disposed in the interstitial spacesdefined by the solid features 112 using any suitable means. For example,the impregnating liquid 120 can be sprayed or brushed onto the texturedsurface 110 (e.g., a texture on an inner surface of a bottle). In someembodiments, the impregnating liquid 120 can be applied to the texturedsurface 110 by filling or partially filling a container that includesthe textured surface 110. The excess impregnating liquid 120 is thenremoved from the container. In some embodiments, the excess impregnatingliquid 120 can be removed by adding a wash liquid (e.g., water) to thecontainer to collect or extract the excess liquid from the container. Insome embodiments, the excess impregnating liquid may be mechanicallyremoved (e.g., pushed off the surface with a solid object or fluid),absorbed or wicked off of the surface 110 using another porous material,and/or removed via gravity or centrifugal forces. In some embodiments,the impregnating liquid 120 can be disposed by spinning the surface 110(e.g., a container) in contact with the liquid (e.g., a spin coatingprocess), and condensing the impregnating liquid 120 onto the surface110. In some embodiments, the impregnating liquid 120 is applied bydepositing a solution comprising the impregnating liquid and one or morevolatile liquids (e.g., depositing via any of the previously describedmethods) and subsequently evaporating away one or more of the volatileliquids.

In some embodiments, the impregnating liquid 120 can be applied using anexternal liquid that spreads or pushes the impregnating liquid along thesurface 110. For example, the impregnating liquid 120 (e.g., ethyloleate) and spreading liquid (e.g., water) may be combined in acontainer and agitated, sonicated, and/or stirred. The fluid flow withinthe container may distribute the impregnating liquid 120 around thecontainer, allowing it to impregnate the solid features 112.

In some embodiments, the impregnating liquid may be nontoxic foroccasional contact with skin because it the liquids relative inertness.These materials may not be safe to eat however, but they could besuitable in many industrial applications or health and beautyapplications. For example these materials 120 can include, silicone oil,a perfluorocarbon liquid, a perfluorinated vacuum oil (such as Krytox1506 or Fomblin 06/6), a fluorinated coolant (e.g.,perfluoro-tripentylamine sold as FC-70, manufactured by 3M), an ionicliquid, a fluorinated ionic liquid that is immiscible with water, asilicone oil comprising polydimethylsiloxane (PDMS), a silicone oil(e.g., fluorinated), fluorosilicone oil, a liquid metal, a syntheticoil, mineral oil, a vegetable oil, halocarbon oil, anelectro-rheological fluid, a magneto-rheological fluid, a ferrofluid, adielectric liquid, a hydrocarbon liquid, a fluorocarbon liquid (e.g.,fluorocarbon oils, such as polyhexafluoropropylene oxide, propene,1,1,2,3,3,3-hexa-fluoro oxidized polymerized ortris(perfluorobut-1-yl)amine), a refrigerant, a vacuum oil, aphase-change material, a semi-liquid, grease, synovial fluid, bodilyfluid, or any other aqueous fluid, or any other impregnating liquiddescribed herein. In some embodiments the following nontoxic liquids canbe used: oleic acid, linoleic acid, triacetin, ethyl linoleate,glycerol, tributryn, tripropionin, dimethicone, perfluorononyldimethicone, silicone fluids, amyl phthalate, any other nontoxic liquidand any combination thereof.

The ratio of the solid features 112 (e.g., particles) to theimpregnating liquid 120 (such ratio referred to, in some embodiments, as“phi,” or “φ”) can be configured to minimize the occurrence of portionsof the solid features 112 protruding above the liquid-product interface.For example, in some embodiments, the solid features 112 make up apercentage of a surface area of the surface 110, with respect to theimpregnating liquid, of less than about 15%, or less than about 5%. Insome embodiments, the percentage of a surface area of the surface 110comprising the solid features 112 can be less than about 50%, about 45%,about 40%, about 35%, about 30%, about 25%, about 20%, about 15%, about10%, about 5%, or less than about 2%. In some embodiments, thepercentage of a surface area of the surface 110 comprising the solidfeatures 112 can be in the range of about 5% to about 50%, about 10% toabout 30%, or about 15% to about 20%, inclusive of all rangestherebetween. In some embodiments, the ratio of the solid features 112to the impregnating liquid 120 can be less than about 0.5, about 0.45,about 0.4, about 0.35, about 0.3, about 0.25, about 0.2, about 0.15,about 0.1, about 0.05, or less than about 0.02. In some embodiments, theratio of the solid features 112 to the impregnating liquid 120 can be inthe range of about 0.05 to about 0.5, about 0.1 to about 0.3, or about0.15 to about 0.2, inclusive of all ranges therebetween. In someembodiments, a low ratio can be achieved using surface textures that aresubstantially pointed. By contrast, surface textures that are flat mayresult in higher ratios, with too much solid material being exposed atthe surface. In some embodiments, the film dry weight is between about5×10⁻⁵ g/cm² and about 10×10⁻⁵ g/cm², between about 0.1×10⁻⁵ g/cm² andabout 5×10⁻⁵ g/cm², between about 10×10⁻⁵ g/cm² and about 100×10⁻⁵g/cm², or between about 0.1×10⁻⁵ g/cm² and about 100×10⁻⁵ g/cm², and thecomposition of the liquid-impregnated surface is between 3% and 5%solids, between 5% and 10%, between 10% and 20%, between 20% and 50%, orbetween 50% and 70%.

In some embodiments, the surface 110 may be characterized by its“complexity,” defined as being equal to (r−1)×100% where r is the Wenzelroughness. Depending on the embodiment, the complexity of the surfacemay be at least 20% (e.g., about 23%), at least 25%, at least 45%, atleast 75%, at least 100%, at least 150%, or at least 200%.

Interaction Between Various Phases in a Liquid-Impregnated Surface

A liquid-impregnated surface that is in contact with a product definesfour distinct phases (or 3 distinct phases in a close environment suchas a pipe, where there is no vapor phase): an impregnating liquid, asurrounding gas (e.g., air), the product and a textured surface. Theinteractions between the different phases determine the morphology ofthe contact line (i.e., the contact line that defines the contact angleof a contact liquid droplet with respect to the liquid-impregnatedsurface). The contact line morphology, in turn, substantially impactsdroplet pinning and mobility of a “contact liquid” on the surface. Somemethods have relied on the complete submersion of a textured surface inan impregnating liquid such as oil by applying excess liquid, in orderto achieve low hysteresis. Although complete submergence may be achievedtemporarily by depositing excess impregnating liquid, eventually thisexcess will drain away (e.g. under gravity) and the liquid-air interfacemay thus eventually come into contact the textured surface. Complete,sustained submergence is possible only if the impregnating liquid isable to completely wet the texture, that is, where θ_(os(a))=0° (whereθ_(os(a)) is the contact angle (this could be an advancing, receding, orstatic contact angle) of the impregnating liquid (subscript ‘o’) on thetextured surface (subscript ‘s’) in the presence of air (subscript ‘a’).The situation is further complicated once a water droplet (or otherexternal phase) is placed on the liquid-impregnated surface, in whichcase the surface will remain submerged in the impregnating liquid onlyif θ_(os(w))=0° as well, where the subscript ‘w’ refers to water.Whether or not θ_(os(a))=0° and θ_(os(w))=0° for a given liquid andtextured substrate material is an important factor that impacts thechoice of an impregnating liquid, for example, the impregnating liquid120, that can/should be used for a particular textured surface. Otherfactors include, for example, properties of the contact liquid thataffect how those materials (e.g., of water and/or product) are shed(whether they roll or slip), and what their shedding velocities are.Moreover, questions related to the longevity of the impregnated liquidfilm and its propensity for depletion, e.g., due to evaporation andentrainment with the droplets (e.g., of water and/or product) beingshed, can have substantial bearing on the configuration of aliquid-impregnated surface, for example, the liquid-impregnated surface100.

Referring now to FIG. 3, a textured surface 210 includes squaremicroposts etched in silicon using standard photolithography processes.A photomask with square windows was used, and the pattern wastransferred to photoresist using UV light exposure. Next, reactive ionetching with inductively-coupled plasma was used to etch the exposedareas to form microposts 212, such that microposts 212 are separated byinterstitial region 214. Each micropost 212 had a square geometry withwidth “a” of about 10 μm, height h of about 10 μm, and varyingedge-to-edge spacing b of about 5, 10, 25, or 50 μm. As shown in FIG. 4,a second level of roughness was produced on microposts 212 by creatingnanograss 216. To create the nanograss, micropost 212 surfaces werecleaned in Piranha solution (a mixture of sulfuric acid and hydrogenperoxide) etched in alternating flow of sulfur hexafluoride (SF₆) andoxygen (O₂) gases for 10 minutes, with an inductively-coupled plasma.The samples were again cleaned in a Piranha solution and treated with alow-energy silane (octadecyltrichlorosilane (OTS)) by solutiondeposition.

Referring now to FIG. 5, the textured surface 210 was impregnated withthe impregnating liquid 220, in this case “BMIm”(1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide) (otherexamples of impregnating liquid may include silicone oil and DI water),by slowly dipping the textured surface (i.e., “dip-coating”) into areservoir of the lubricant. The textured surface 210 was then withdrawnat speed S, at a slow enough rate that capillary numberCa=μ_(o)S/γ_(oa)<10⁻⁵, to ensure that no excess fluid remained on themicropost 212 tops, where μ_(o) is the dynamic viscosity and γ_(oa) isthe surface tension of the impregnating liquid 220. When the advancingangle θ_(adv,os(a)) is less than θ_(c) (see Table 1 below), theimpregnating liquid 220 film will not spontaneously spread into thetextured surface 210, as can be seen for BMIm in FIG. 5. FIG. 6 shows ahigher-magnification view of the region of the textured surfaceindicated by the arrow A in FIG. 5. Visible in FIG. 6 are a portion ofthe nanotextured top surface 616 of a micropost, and a portion of theimpregnating fluid 620. By withdrawing the textured surface 210 from areservoir of BMIm, the impregnating film remains stable, sinceθ_(rec,os(a))<θ_(c) for the microposts 212 with b=5 μm and 10 μm.

Table 1 (below) shows various configurations of features formed on thetextured surface 210, the configurations characterized by “post spacing”(“b”), “ratio of total surface area to the projected area of the solid”(“r”), emerged area fraction (“φ” or “phi”), and critical contact angleθ_(c) defined by θ_(c)=cos⁻¹((1−φ)/(r−φ)); h, a=10 μm. Note that if thetextured surface 210 is not coated with OTS, θ_(os(w))>θ_(c) forimpregnating liquids 220 as well as all b. Thus, water droplets wereexpected to displace the hydrophobic liquid 220 and get impaled by themicroposts 212 leading to significant pinning, and such behavior wasconfirmed, as the droplets did not roll-off of these textured surfaces.

TABLE 1 Post spacing, b (μm) r φ θ_(c) (°) 5 2.8 0.44 76 7.5 2.3 0.33 7010 2.0 0.25 65 25 1.3 0.08 42 50 1.1 .093 26

Referring now to FIGS. 7A-7J, in some embodiments, the impregnatingliquid 220, for example, oil may spread over and “cloak” the contactliquid, for example, a water droplet, as shown in FIG. 7A. Cloaking cancause the progressive loss of the impregnating liquid 220 throughentrainment in the water (or other composition) droplets as they areshed from the surface. The criterion for cloaking is given by thespreading coefficient, S_(ow(a))≡γ_(wa)−γ_(wo)−γ_(oa), where γ is theinterfacial tension between the two phases designated by subscripts w,o, and a. Thus, the expression “S_(ow(a))>0” implies that theimpregnating liquid 220 will cloak the water droplet (FIG. 7A), whereasS_(ow(a))<0 implies otherwise (FIG. 7B). Based on these criterion, twodifferent impregnating liquids 220, were selected: (1) silicone oil, forwhich S_(ow(a))≈6 mN/m, and (2) an ionic liquid(1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide-BMIm) forwhich S_(ow(a))≈−5 mN/m. Ionic liquids have extremely low vaporpressures (˜10⁻¹² mmHg), and therefore they mitigate concern for theloss of impregnating liquid through evaporation. Goniometricmeasurements of the advancing and receding contact angles of theseliquids in the presence of air and water, as well as their interfacialtensions, were performed and are presented in Table 2 and Table 3(below).

TABLE 2 Liquid Substrate θ_(adv, os(a)) (°) θ_(rec, os(a)) (°)θ_(adv, os(w)) (°) θ_(rec, os(w)) (°) Silicone oil OTS-treated silicon 00  20 ± 5 0 BMIm OTS treated silicon 67.8 ± 0.3 60.8 ± 1.0  61.3 ± 3.6 12.5 ± 4.5 DI water OTS-treated silicon 112.5 ± 0.6  95.8 ± 0.5 NA NASilicone oil Silicon 0 0 153.8 ± 1.0  122 ± 0.8 BMIm Silicon 23.5 ± 1.8 9.8 ± 0.9 143.4 ± 1.8 133.1 ± 0.9 DI water Silicon  20 ± 5° 0 NA NA

Table 3 shows surface and interfacial tension measurements and resultingspreading coefficients S_(ow(a))=γ_(wa)−γ_(ow)−γ_(oa) of 9.34, 96.4, and970 cP for Dow Corning PMX 200 Silicone oils on water in air. Values ofγ_(ow) were provided by Dow Corning.

TABLE 3 γ_(ow) γ_(oa) γ_(wa) S_(ow(a)) Liquid (mN/m) (mN/m) (mN/m)(mN/m) Silicone oil 46.7 20.1 72.2 5.4 (9.34 cP, 96.4 cP) Silicone oil45.1 21.2 72.2 5.9 (970 cP)

FIG. 7C shows an 8 μl water droplet placed on the silicone oilimpregnated textured surface 210. The droplet forms a large apparentcontact angle (˜100 degrees), but very close to the solid surface (redarrows in FIG. 7 c) its profile changes from convex to concave. When afluorescent dye was added to the silicone oil and imaged under UV light,it was observed that the point of inflection (i.e., the profile changenoted above) corresponded to the height to which an annular ridge ofsilicone oil was pulled up in order to satisfy a vertical force balanceof the interfacial tensions at the inflection point (FIG. 7E). Althoughthe oil was expected to have spread over the entire droplet (FIG. 7C),the cloaking film was too thin to be captured in these images. The“wetting ridge” was also observed in the case of ionic liquid (FIG. 7Dand FIG. 7F). Such wetting ridges are reminiscent of those observedaround droplets on soft substrates.

As described herein, the textured surface 210 can be completelysubmerged in the impregnating liquid 220 if θ_(os(a))=0°. This conditionwas found to be true for silicone oil, implying that the tops of themicroposts 212 should be covered by a stable thin oil film. This filmwas observed experimentally using laser confocal fluorescence microscopy(LCFM); the micropost 212 tops appear bright due to the presence of afluorescent dye that was dissolved in the oil (FIG. 7G). EnvironmentalSEM images of the surface (FIG. 7I) show the oil-filled texture, andconfirm that this film is less than a few microns thick, consistent withprior estimates for completely-wetting films. On the other hand, BMImhas a non-zero contact angle on a smooth OTS-coated silicon surface(θ_(os(a))=65±5°), indicating that with this impregnating liquid, thepost tops should remain dry. Indeed, LCFM images confirmed this (FIG.7H)—the post tops appear dark because there is no dye present tofluoresce. Since BMIm is conductive and has an extremely low vaporpressure, it can be imaged in a SEM. As shown in FIG. 7J, discretedroplets resting on micropost tops are seen, confirming that a thin filmwas not stable on the post tops in this case.

Stable Configuration of Contact Liquid Droplets on Liquid-ImpregnatedSurfaces

As shown in FIG. 7B, in the case of BMIm there are three distinct3-phase contact lines at the perimeter of the drop that confine thewetting ridge: the oil-water-air contact line, the oil-solid-air contactline outside the drop, and the oil-solid-water contact line underneaththe drop. These contact lines exist because θ_(os(a))>0, θ_(os(w))>0,and S_(ow(a))<0. In contrast, in the case of silicone oil (FIG. 7A),none of these contact lines exist because θ_(os(a))=0, θ_(os(w))=0, andS_(ow(a))>0. These configurations are just two of the 12 differentconfigurations in such a four-phase system where impregnation byimpregnating liquid 220 is possible. These configurations are discussedbelow.

A thermodynamic framework is outlined that can predict which of theabove-noted 12 states will be stable for a given contact liquid droplet,impregnating liquid 220, and textured surface 210 substrate material.There are three possible configurations to consider for the interface“outside” of the droplet (i.e., not directly adjacent to or beneath thedroplet, but rather spaced from the droplet, e.g., horizontally) (i.e.,in an air environment), and three possible configurations to considerfor the interface “underneath the droplet” (e.g., in a waterenvironment). These configurations are shown in FIG. 8, along with thetotal interface energy of each configuration. The configurationspossible outside the droplet are A1 (not impregnated, i.e. dry), A2(impregnated with emergent features), and A3 (impregnated with submergedfeatures—i.e. encapsulated). On the other hand, underneath the droplet,the possible configurations are W1 (impaled), W2 (impregnated withemergent features), and W3 (impregnated with submerged features—i.e.encapsulated). The stable configuration will be the one that has thelowest total interface energy.

First, the configurations outside of the droplet are focused on. Atextured surface, for example, textured surface 210, is slowly withdrawnfrom a reservoir of oil. The resulting surface could be in any of statesA1, A2, and A3 depending on which has the lowest energy. For example,state A2 would be stable if it has the lowest total interface energy,i.e. E_(A2)<E_(A1), E_(A3). From FIG. 8, this results in:

E _(A2) <E _(A1)

(γ_(sa)−γ_(os))/γ_(oa)>(1−φ)/(r−φ)  (1)

E _(A2) <E _(A3)

γ_(sa)−γ_(os)−γ_(oa)<0  (2)

where φ is the fraction of the projected area of the surface that isoccupied by the solid and r is the ratio of total surface area to theprojected area of the solid. In the case of square posts with width a,edge-to-edge spacing b, and height h, φ=a²/(a+b)² and r=1+4ah/(a+b)².Applying Young's equation, cos(θ_(os(a)))=(γ_(sa)−γ_(os))/γ_(oa), Eq.(1) reduces to the hemi-wicking criterion for the propagation of a oilthrough a textured surface: cos(θ_(os(a)))>(1−φ)/(r−φ)=cos(θ_(c)). Thisrequirement can be conveniently expressed as θ_(os(a))<θ_(c). In Eq.(2), γ_(sa)−γ_(os)−γ_(oa), is simply the spreading coefficient S_(os(a))of oil on the textured surface in the presence of air. This can bereorganized as (γ_(sa)−γ_(os))/γ_(oa)<1, and applying Young's equationagain, Eq. (2) can be written as θ_(os(a))>0. Expressing Eq. (1) interms of the spreading coefficient S_(os(a)), yields:−γ_(oa)(r−1)/(r−φ)<S_(os(a)). The above simplifications then lead to thefollowing equivalent criteria for the surface to be in state A2:

E _(A2) <E _(A1) ,E _(A3)

θ_(c)>θ_(os(a))>0

−γ_(oa)(r−1)/(r−φ)<S _(os(a))<0  (3)

Similarly, state A3 would be stable if E_(A3)<E_(A2), E_(A1). From FIG.8, this gives:

E _(A3) <E _(A2)

θ_(os(a))=0

γ_(sa)−γ_(os)−γ_(oa) ≡S _(os(a))≧0  (4)

E _(A3) <E _(A1)

θ_(os(a))<cos⁻¹(1/r)

S _(os(a))>−γ_(oa)(1−1/r)  (5)

Note that Eq. (5) is automatically satisfied by Eq. (4), thus thecriterion for state A3 to be stable (i.e. encapsulation) is given by Eq.(4). Following a similar procedure, the condition for state A1 to bestable can be derived as:

E _(A1) <E _(A2) ,E _(A3)

θ_(os(a))>θ_(c)

S _(os(a))<−γ_(oa)(r−1)/(r−φ)  (6)

Note that the rightmost expression of Eq. (4) can be rewritten as(γ_(sa)−γ_(os))/γ_(oa)≧1. Young's equation would suggest that ifθ_(os(a))=0, then (γ_(sa)−γ_(os))/γ_(oa)=1 (i.e. S_(os(a))=0). However,θ_(os(a))=0 is also true for the case that (γ_(sa)−γ_(os))/γ_(oa)>1(i.e. S_(os(a))>0). Young's equation predicts the contact angle based onbalancing the surface tension forces on a contact line, such that theequality only exists for a contact line at static equilibrium. For aspreading film (S_(os(a))>0) a static contact line doesn't exist, henceprecluding the applicability of Young's equation.

Referring now to the configurations possible underneath the droplet,upon contact with water, the interface beneath the droplet will attainone of the three different states—W1, W2, or W3 (FIG. 8)—depending onwhich has the lowest energy. Applying the same method to determine thestable configurations of the interface beneath the droplet as describedherein, and using the total interface energies provided in FIG. 8, thestability requirements take a form similar to Eqs (3), (4), and (6),with γ_(oa), γ_(sa), θ_(os(a)), S_(os(a)), replaced with γ_(ow), γ_(sw),θ_(os(w)), S_(os(w)) respectively. θ_(c) is not affected by thesurrounding environment as it is only a function of the textureparameters, φ and r. Thus, the texture will remain impregnated with oilbeneath the droplet with emergent post tops (i.e. state W2) when:

E _(W2) <E _(W1) ,E _(W3)

θ_(c)>θ_(os(w))>0

−γ_(ow)(r−1)/(r−φ)<S _(os(w))<0  (7)

State W3 will be stable (i.e. the oil will encapsulate the texture)when:

E _(W3) <E _(W1) ,E _(W2)

θ_(os(w))=0

γ_(sw)−γ_(os)−γ_(ow) ≡S _(os(w))≧0.  (8)

and the droplet will displace the oil and be impaled by the textures(state W1) when:

E _(W1) <E _(W2) ,E _(W3)

θ_(os(w))>θ_(c)

S _(os(w))<−γ_(ow)(r−1)/(r−φ)  (9)

Combining the above criteria along with the criterion for cloaking ofthe water droplet by the oil film described herein, the various possiblestates can be organized in a regime map, as shown in FIG. 9. Thecloaking criterion is represented by the upper two schematic drawings.For each of these cases, six different configurations are possibledepending on how the oil interacts with the surface texture in thepresence of air (vertical axes in FIG. 9) and water (horizontal axes inFIG. 9). The vertical and horizontal axes are the normalized spreadingcoefficients S_(os(a))/γ_(oa) and S_(os(w))/γ_(ow) respectively.Considering first the vertical axis of FIG. 9, whenS_(os(a))/γ_(oa)<−(r−1)/(r−φ) (i.e., when Eq. (6) holds), oil does notimpregnate the texture. As S_(os(a))/γ_(oa) increases above thiscritical value, impregnation becomes feasible but the post tops arestill left emerged. Once S_(os(a))/γ_(oa)>0, the post tops are alsosubmerged in the oil leading to complete encapsulation of the texture.Similarly, on the x-axis of FIG. 9, moving from left to right, asS_(os(w))/γ_(ow) increases, the droplet transitions from an impaledstate to an impregnated state to a fully-encapsulated state.

FIG. 9 shows that there can be up to three different contact lines, twoof which can get pinned on the texture. The degree of pinning determinesthe roll-off angle α*, the angle of inclination at which a dropletplaced on the textured solid begins to move. Droplets that completelydisplace the oil (states A3-W1, A2-W1 in FIG. 8) are not expected toroll off the surface. These states are achieved when θ_(os(w))>θ_(c) asis the case for both BMI-Im and silicone oil impregnated surfaces whenthe silicon substrates are not treated with OTS (see Table 1). Asexpected, droplets did not roll off of these surfaces. Droplets instates with emergent post tops (A3-W2, A2-W2, A2-W3) are expected tohave reduced mobility that is strongly texture dependent, whereas thosein states with encapsulated posts outside and beneath the droplet (theA3-W3 states in FIG. 8) are expected to exhibit no pinning andconsequently infinitesimally small roll-off angles.

FIG. 10A shows measurements of roll-off angles for 5 μL water dropletson silicone oil impregnated and BMIm impregnated textures, with varyingpost spacing b. For comparison, the same textures without animpregnating liquid (no impregnating liquid, which is the conventionalsuper impregnating case) were also evaluated. The silicone oilencapsulated surfaces have extremely low roll-off angles regardless ofthe post spacing b and oil viscosity, showing that contact line pinningwas negligible, as predicted for a liquid droplet in an A3-W3 state withno contact lines on the textured substrate. On the other hand, BMImimpregnated textures showed much higher roll-off angles, which increasedas the spacing decreased—a trend that is similar to Cassie droplets onsuper impregnating surfaces. This observation shows that pinning wassignificant in this case, and occurs on the emergent post tops. (asshown in FIG. 10B). Pinning on BMIm impregnated textures wassignificantly reduced by adding a second smaller length scale texture(i.e. nanograss) to the posts, so that BMIm impregnated the texture evenon the post tops, thereby substantially reducing φ (FIG. 10C). Theroll-off angle decreased from over 30 degrees (for BMIm impregnatedposts without nanotexture) to only about 2 degrees (for BMIm impregnatedposts with nanotexture). Note that the reduction in the emergent areafraction φ is not due to the absolute size of the texture features,since the oil-water and oil-air interfaces intersect surface features atcontact angles θ_(os(w)) and θ_(os(a)), and φ depends on these contactangles and feature geometry.

The effect of texture on the roll-off angle can be modeled by balancinggravitational forces with pinning forces. A force balance of a waterdroplet on a smooth solid surface at incipient motion gives ρ_(w)Ωg sinα*≈2R_(b)γ_(wa) (cos θ_(rec,ws(a))−cos θ_(adv,ws(a))), where ρ_(w) isthe density of the liquid droplet of volume Ω, g is the gravitationalacceleration, R_(b) is the droplet base radius, and θ_(adv,ws(a)) andθ_(rec,ws(a)) are the advancing and receding contact angles of dropletin air on the smooth solid surface. Pinning results from contact anglehysteresis of up to two contact lines: an oil-air-solid contact linewith a pinning force per unit length given by γ_(oa) (cosθ_(rec,os(a))−cos θ_(adv,os(a))), and an oil-water-solid contact linewith a pinning force per unit length given by γ_(ow) (cosθ_(rec,os(w))−cos θ_(adv,os(w))). The length of the contact line overwhich pinning occurs is expected to scale as R_(b) φ^(1/2) where φ^(1/2)is the fraction of the droplet perimeter (˜R_(b)) making contact withthe emergent features of the textured substrate. Thus, a force balancetangential to the surface gives:

ρ_(w) Ωg sin α*˜R_(b)φ^(1/2)[γ_(ow)(cos θ_(rec,os(w))−cosθ_(adv,os(w)))+γ_(oa)(cos θ_(rec,os(a))−cos θ_(adv,os(a)))]  (10)

Dividing Eq. (10) by R_(b)γ_(wa) we obtain a non-dimensional expression:

Bo sin α*f(θ)˜φ^(1/2)[γ_(ow)(cos θ_(rec,os(w))−cosθ_(adv,os(w)))+γ_(oa)(cos θ_(rec,os(a))−cos θ_(adv,os(a)))]/γ_(wa)  (11)

where f(θ)=Ω^(1/3)/R_(b)=[(π/3)(2+cos θ)(1−cos θ)²/sin³θ)]^(1/3) byassuming the droplet to be a spherical cap making an apparent contactangle θ with the surface. Bo=Ω^(2/3)ρ_(w)g/γ_(wa) is the Bond number,which compares the relative magnitude of gravitational forces to surfacetension forces. Values for θ_(rec,os(w)), θ_(adv,os(w)), θ_(rec,os(a)),θ_(adv,os(a)), γ_(ow), γ_(oa), and γ_(wa) are provided in Tables 2 and3. FIG. 10D shows that the measured data is in reasonable agreement withthe scaling of Eq. (11). The data for the silicone oil encapsulatedsurface and for the BMIm impregnated, nanograss-covered posts, lie closeto the origin as both φ and α* are very small in these cases.

Dynamics of Droplet Shedding

Once gravitational forces on a droplet overcome the pinning forces, thevelocity attained by the droplet determines how quickly it can be shed,which reflects the non-wetting performance of the surface. For a dropletof volume Ω, this velocity would be expected to depend on both thecontact line pinning and viscosity of the lubricant. The steady-stateshedding velocity V of water droplets was measured using a high-speedcamera while systematically varying lubricant dynamic viscosity μ_(o),post spacing b, textured surface tilt angle α, and droplet volume, Ω.These measurements are shown in FIG. 11A, where V is plotted as afunction of a for different μ_(o), b, and Ω. As shown in FIG. 11A, thevelocity V increases with α and Ω because both increase thegravitational force acting on the droplet. As also shown in FIG. 11A, Vdecreases with μ_(o) and φ because both increase the resistance todroplet motion.

To explain these trends, it is first determined whether the droplet isrolling or sliding. Consider the oil-water interface beneath the dropletas shown in FIG. 11B. The shear stress at this interface, on the waterside, scales as τ_(w)˜μ_(w)(V−V_(i))/h_(cm), and on the oil side theshear stress scales as τ_(o)˜μ_(o)V_(i)/t, where V_(i) is the velocityof the oil-water interface, h_(cm) is the height of the centre of massof the droplet above the solid surface, and t is the thickness of theoil film. Since τ_(w) must be equal to τt_(o) at the oil-waterinterface, μ_(w)(V−V_(i))/h_(cm)˜μ_(o)V_(i)/t. Rearranging this gives:

$\begin{matrix}{{V_{i}/V} \sim \left( {1 + {\frac{\mu_{o}}{\mu_{w}}\frac{h_{cm}}{t}}} \right)^{- 1}} & (12)\end{matrix}$

Since (μ_(o)/μ_(w))(h_(cm)/t)>>1 as described herein, V_(i)/V<<1, i.e.the oil-water interface moves at a negligibly small velocity relative tothat of the droplet's centre of mass. This suggests that the dropletsbeing shed on the textured surface, for example, textured surface 210,are rolling. This was further confirmed by adding ground coffeeparticles to the water droplet and tracking their motion relative to thedroplet with a high-speed camera as the droplet moved across thesurface. Particle trajectories, shown in FIG. 11C, clearly show that thedroplets roll across the liquid-impregnated surface as they are shed(μ_(o)=96.4 cP).

To determine the magnitude of V, the rate of change of gravitationalpotential energy is balanced as the droplet rolls down the incline withthe total rate of energy dissipation due to contact line pinning andviscous effects. The resulting energy balance gives:

$\begin{matrix}{{V\left( {F_{g} - F_{p}} \right)} \sim {{\mu_{w}{\int_{\Omega_{drop}}{\left( {\nabla\; \overset{\_}{u}} \right)_{drop}^{2}\ {\Omega}}}} + {\mu_{o}{\int_{\Omega_{film}}{\left( {\nabla\; \overset{\_}{u}} \right)_{film}^{2}\ {\Omega}}}} + {\mu_{o}{\int_{\Omega_{ridge}}{\left( {\nabla\; \overset{\_}{u}} \right)_{ridge}^{2}\ {\Omega}}}}}} & (13)\end{matrix}$

where F_(g) and F_(p) represent the net gravitational and pinning forcesacting on the droplet, the Ω terms are the volume over which viscousdissipation occurs, and the ∇ū terms are the corresponding velocitygradients. The form of Eq. (13) is similar to that for viscous dropletsrolling on completely non-wetting surfaces though additional terms arepresent due to the presence of the impregnated oil. The three terms onthe right side of Eq. (13) represent the rate of viscous dissipationwithin the droplet (I), in the oil film beneath the droplet (II), and inthe wetting ridge near the three-phase contact line (III).

The rate of viscous dissipation within the droplet (I) is primarilyconfined to the volume beneath its center of mass and can beapproximated as I˜μ_(w)(V/h_(cm))²R_(b) ²h_(cm), where R_(b) is the baseradius of the droplet. Applying geometrical relations for a sphericalcap, R_(b)/h_(cm)=g(θ)=4/3(sin θ)(2+cos θ)/(1+cos θ)² results in:

I˜μ _(w) V ² R _(b) g(θ)

The rate of viscous dissipation within the film (II) can be approximatedas II˜μ_(o)(V_(i)/t)²R_(b) ²t. Since (μ_(w)/μ_(o))(t/h_(cm))<<1, fromEq. (12) ∇ū_(film)˜V_(i)/t˜(μ_(w)/μ_(o))(V/h_(cm)). Usingh_(cm)=R_(b)/g(θ), the rate of viscous dissipation within the film (II)can be rewritten, such that:

${II} \sim {\frac{\mu_{w}^{2}}{\mu_{o}}{V^{2}\left\lbrack {g(\theta)} \right\rbrack}^{2}t}$

Finally, the rate of viscous dissipation in the wetting ridge (III) canbe approximated as III˜μ_(o)(V/h_(ridge))²R_(b)h_(ridge) ² since fluidvelocities within the wetting ridge must scale as the velocity of thecentre of mass and vanish at the solid surface, giving velocitygradients that scale as ∇ū_(ridge)˜V/h_(ridge), where h_(ridge) is theheight of the wetting ridge. Thus,

III˜μ _(o) V ² R _(b).

Noting that F_(g)=ρ_(w)Ωg sin α and F_(p)=ρ_(w)Ωg sin α* and dividingboth sides of Eq. (13) by R_(b)Vγ_(wa) yields

$\begin{matrix}{{{{Bo}\left( {{\sin \; \alpha} - {\sin \; \alpha^{*}}} \right)}{f(\theta)}} \sim {{Ca}\left\{ {{g(\theta)} + {\left\lbrack {g(\theta)} \right\rbrack^{2}\frac{\mu_{w}}{\mu_{o}}\frac{t}{R_{b}}} + \frac{\mu_{o}}{\mu_{w}}} \right\}}} & (14)\end{matrix}$

Where Ca=μ_(w)V/γ_(wa), is the capillary number, Bo=,Ω^(2/3)ρ_(w)g/γ_(wa) is the Bond number, and f(θ)=Ω^(1/3)/R_(b)(described before herein). Since (μ_(w)/μ_(o))(t/R_(b))<<1, andμ_(o)/μ_(w)>>g(θ) in our experiments, Eq. (14) can be simplified to:

$\begin{matrix}{{{{Bo}\left( {{\sin \; \alpha} - {\sin \; \alpha^{*}}} \right)}{f(\theta)}} \sim {{Ca}\frac{\mu_{o}}{\mu_{w}}}} & (15)\end{matrix}$

The datasets shown in FIG. 11A were organized according to Eq. (15) andwere found to collapse onto a single curve (FIG. 1 ID), demonstratingthat the above scaling model captures the essential physics of thephenomenon: the gravitational potential energy of the rolling droplet isprimarily consumed in viscous dissipation in the wetting ridge aroundthe base of the rolling droplet. Similar conclusions apply to solidspheres rolling on thin films of viscous oil. Furthermore, Eq. (14) andEq. (15) apply for cloaked and uncloaked droplets, because inertial andgravitational forces in the cloaking films are very small. Consequently,the velocity is uniform across the film and viscous dissipation isnegligible.

In some embodiments, the φ can be less than about 0.30, about 0.25,about 0.20, about 0.15, about 0.10, about 0.05, about 0.01, or less thanabout 0.005. In some embodiments, φ can be greater than about 0.001,about 0.005, about 0.01, about 0.05, about 0.10, about 0.15, or greaterthan about 0.20. In some embodiments, φ can be in the range of about 0to about 0.25. In some embodiments, φ can be in the range of about 0 toabout 0.01. In some embodiments, φ can be in the range of about 0.001 toabout 0.25. In some embodiments, φ can be in the range of about 0.001 toabout 0.10.

In some embodiments, a liquid-impregnated surface, for example theliquid-impregnated surface 100, 200, or any of the liquid-impregnatedsurfaces described herein can be configured such that cloaking by theimpregnating liquid can either be eliminated or induced. Without beingbound to any particular theory, impregnating liquids that have S_(ow(a))less than 0 will not cloak, resulting in no loss of impregnatingliquids, whereas impregnating liquids that have S_(ow(a)) greater than 0will cloak a product P in contact with the liquid-impregnated surface(e.g., food products, drugs, health and beauty products, water,bacterial colonies, etc.) and this may be exploited to preventcorrosion, fouling, etc. In some embodiments, cloaking can be used forpreventing vapor-liquid transformation (e.g., water vapor, metallicvapor, etc.). In some embodiments, cloaking can be used for inhibitingliquid-solid formation (e.g., ice, metal, etc.). In some embodiments,cloaking can be used to make reservoirs for carrying the materials, suchthat independent cloaked materials can be controlled and directed byexternal means (like electric or magnetic fields).

In some embodiments, cloaking can be desirable and can be used as ameans for preventing environmental contamination, like a time capsulepreserving the contents of the cloaked material. Cloaking can result inencasing of the material thereby cutting its access from theenvironment. This can be used for transporting materials (e.g.,bioassays) across a length in a way that the material is notcontaminated by the environment.

In some embodiments, the amount of cloaking can be controlled by variouslubricant properties such as viscosity, surface tension of theimpregnating liquid. Additionally or alternatively, the de-wetting ofthe cloaked material can also be controlled to release the material, forexample a system in which a product is disposed on theliquid-impregnated surface at one end, and upon reaching the other endis exposed to an environment that causes the product to uncloak.

In some embodiments, the impregnating liquid can be selected to have aS_(ow(a)) less than 0.

In some embodiments, liquid-impregnated surfaces described herein canhave advantageous droplet roll-off properties that minimize theaccumulation of the contacting liquid on the surfaces. Without beingbound to any particular theory, a roll-off angle “α” of theliquid-impregnated surface in some embodiments can be less than about50°, less than about 40°, less than about 30°, less than about 25°, orless than about 20°.

Typically, flow through a pipe or channel having a liquid-impregnatedsurface on its interior can be described by the following equation:

Q/(Δp/L)˜(R ⁴/μ₁)(1+C(h/r)(μ₁/μ₂)  (16)

where Q is the volumetric flow rate, R is pipe radius, h is the heightof the texture, μ₂ is the viscosity of lubricant and μ₁ is the viscosityof the fluid flowing through the pipe. C is a constant that relates tothe obstruction of the flow of the impregnating liquid due to thetexture. C=1 in the limit of infinitely sparse textures (no texture),and C approaches 0 for very tightly spaced textures. Δp/L is thepressure drop per L. Note that C*h*(μ₁/μ₂) defines a slip length, b.Without being bound to any particular theory, it is believed that(h/R)(μ₁/μ₂) should be greater than 1 for the texture to have asignificant effect on flow, and this sets the height of the texture inrelation to the viscosity ratio.

Power˜(Δp/L)*Q(here “˜” means “scales as”)

So equation (16) becomes:

$\begin{matrix}{\frac{Q^{2}}{Power} \sim {\left( \frac{R^{4}}{\mu_{1}} \right)\left\lbrack {1 + {{C\left( \frac{t}{R} \right)}\left( \frac{\mu_{1}}{\mu_{2}} \right)}} \right\rbrack}} & (17)\end{matrix}$

Then the ratio of the flow rate of a liquid without the coating to onewith the coating, at the same pumping power, is:

$\begin{matrix}{\frac{Q_{coated}}{Q_{uncoated}} \sim \left\lbrack {1 + {{C\left( \frac{h}{R} \right)}\left( \frac{\mu_{1}}{\mu_{2}} \right)}} \right\rbrack^{\frac{1}{2}}} & (18)\end{matrix}$

Or the reduction in power require to achieve the same flow rate is:

$\begin{matrix}{\frac{P_{coated}}{P_{uncoated}} \sim \left\lbrack {1 + {{C\left( \frac{h}{R} \right)}\left( \frac{\mu_{1}}{\mu_{2}} \right)}} \right\rbrack^{- 1}} & (19)\end{matrix}$

If h<<R, then the flow of the product also drags the material within thefilm at a flow rate Q_(f) given by:

Q _(f) /Q=h/R[2b/R+(b/R)]/[½+2b/R+(b/R)²]  (20)

If b/R<<1 then:

Q _(f) /Q˜4hb/R ²(valid for h<R and b/R)  (21)

Although modeled for pipe flow, the general principals discussed abovealso apply to open systems, for example, product containers, where R isreplaced with the characteristic depth of the flowing material. Theaverage velocity of the flow ˜Q/A, where A is the cross-sectional areaof the flowing fluid.

For example, mayonnaise, which is a Bingham plastic, has a viscositythat approaches infinity at low shear rates (it is non-Newtonian), andtherefore behaves like a solid as long as shear stress within it remainsbelow a critical value. By way of comparison, for honey, which isNewtonian, the flow is much slower. For both systems, h and R are of thesame order of magnitude, and μ₂ is the same. However, since

μ_(honey)<<μ_(mayonnaise),then(h/R)(μ_(honey)/μ₂)<<(h/R)(μ_(mayonnaise)/μ₂)

thus mayonnaise flows much more quickly out of the bottle than honey. Insome embodiments, μ₁/μ₂ can be greater than about 1, about 0.5, or about0.1.

In some embodiments, the impregnating liquid includes an additive toprevent or reduce evaporation of the impregnating liquid, for example asurfactant. The surfactants can include, but are not limited to,docosenoic acid, trans-13-docosenoic acid, cis-13-docosenoic acid,nonylphenoxy tri(ethyleneoxy)ethanol, methyl 12-hydroxyoctadecanate,1-Tetracosanol, fluorochemical “L-1006”, and any combination thereof.Examples of surfactants described herein and other surfactants which canbe included in the impregnating liquid can be found in White, I.,“Effect of Surfactants on the Evaporation of Water Close to 100 C,”Industrial & Engineering Chemistry Fundamentals 15.1 (1976): 53-59, thecontent of which is incorporated herein by reference in its entirety. Insome embodiments, the additives can include C₁₆H₃₃COOH, C₁₇H₃₃COOH,C₁₈H₃₃COOH, C₁₉H₃₃COOH, C₁₄H₂₉OH, C₁₆H₃₃OH, C₁₈H₃₇OH, C₂₀H₄₁OH,C₂₂H₄₅OH:, C₁₇H₃₅COOCH, C₁₅H₃₁COOC₂H₅, C₁₆H₃₃OC₂H₄OH, C₁₈H₃₇OC₂H₄OH,C₂₀H₄₁OC₂H₄OH, C₂₂H₄₅OC₂H₄OH. Sodium docosyl sulfate, poly(vinylstearate), Poly (octadecyl acrylate), Poly(octadecyl methacrylate) andany combination thereof. Further examples of additives can be found inBarnes, G. T., “The potential for monolayers to reduce the evaporationof water from large water storages,” Agricultural Water Management 95.4(2008): 339-353, the content of which is hereby by incorporated hereinby reference in its entirety.

Non-Toxic Liquid-Impregnated Surfaces

In some embodiments, any of the liquid-impregnated surfaces describedherein can include non-toxic materials, for example impregnating liquidand/or solid (e.g., solid particles used to form solid features such as,for example, wax), that are non-toxic to humans and/or animals.Non-toxic liquid-impregnated surfaces can therefore be safely disposedon surfaces, for example the interior surface(s) of containers that areconfigured to house products formulated for human use or consumption.Such products can include, for example food products, drugs (e.g., FDAapproved drugs), or health and beauty products.

In some embodiments, the solid features (e.g., solid particles) and/orthe impregnating liquid can be removed or depleted from the surface dueto friction and abrasion due to product sliding over theliquid-impregnated surface. The impregnating liquid may be particularlyprone to being depleted from the surface by entrainment within theproduct or dissolution into the product. The concentration of thedepleted impregnating liquid entrained in the product can be in therange of about 5 ppm to about 500 ppm, which is not negligible.Therefore, there is a need for liquid impregnating surfaces that includeimpregnating liquid and/or solids (e.g., solid particles that form thesolid features) that are non-toxic and safe for human use orconsumption. In some embodiments, any solvents used in the processing ofany components of the liquid-impregnated surface, for example the solidsurface, may remain in the liquid-impregnated surface in someconcentration, and thus the solvents can also be chosen to be non-toxic.Examples of solvents that are nontoxic in residual quantities includeethyl acetate, ethanol (e.g., 200 proof, 140 proof), water, or any othernon-toxic solvent. In other embodiments, the solvent may comprise ethylacetate and/or heptane.

The non-toxicity requirements can vary depending upon the intended useof the product in contact with the liquid-impregnated surface. Forexample, liquid-impregnated surfaces configured to be used with foodproducts or products classified as drugs would be required to have amuch higher level of non-toxicity when compared with products meant tocontact only the oral mucosa (e.g., toothpaste, mouth wash, etc.), orapplied topically such as, for example, health and beauty products(e.g., hair gel, shampoo, lotion, cosmetics, etc.).

In some embodiments, the non-toxic liquid-impregnated surface can bedisposed on a substrate, for the example, the interior wall of acontainer configured to house a food product or an ingredient of a foodproduct for consumption by a human or an animal. In some embodiments,the substrate can be any surface, for example a surface of a foodprocessing equipment that makes contact with food or food ingredients.The food product or food ingredient can include, for example, a sticky,highly viscous, and/or non-Newtonian food product. Such food productscan include, for example, candy, chocolate syrup, mash, yeast mash, beermash, taffy, food oil, fish oil, marshmallow, dough, batter, bakedgoods, chewing gum, bubble gum, butter, peanut butter, jelly, jam,dough, gum, cheese, cream, cream cheese, mustard, yogurt, sour cream,curry, sauce, ajvar, currywurst sauce, salsa lizano, chutney, pebre,fish sauce, tzatziki, sriracha sauce, vegemite, chimichurri, HPsauce/brown sauce, harissa, kochujang, hoisin sauce, kim chi, cholulahot sauce, tartar sauce, tahini, hummus, shichimi, ketchup, mustard,pasta sauce, Alfredo sauce, spaghetti sauce, icing, dessert toppings, orwhipped cream, liquid egg, ice cream, animal food, any other foodproduct or combination thereof. In such embodiments, the components ofthe non-toxic liquid-impregnated surfaces can include materials that arenon-toxic when consumed orally by a human or an animal. For example, theliquid-impregnated surface can include materials that are a U.S. Foodand Drug Administration (FDA) approved direct or indirect food additive,an FDA approved food contact substance, satisfy FDA regulatoryrequirements to be used as a food additive or food contact substance,and/or is an FDA GRAS material. Examples of such materials can be foundwithin the FDA Code of Federal Regulations Title 21, located at“http://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/cfrsearch.cfm,”the entire contents of which are hereby incorporated by referenceherein. In some embodiments, the components of the non-toxicliquid-impregnated surface, for example the impregnating liquid, canexist as a component of the food product disposed within the container.In some embodiments, the components of the non-toxic liquid-impregnatedsurface can include a dietary supplement or ingredient of a dietarysupplement. The components of the non-toxic liquid-impregnated surfacecan also include an FDA approved food additive or color additive. Insome embodiments, the non-toxic liquid impregnating surface can includematerials that exist naturally in, or are derived from plants andanimals. In some embodiments, the non-toxic liquid-impregnated surfacefor use with food products includes solids or impregnating liquid thatare flavorless or have a high flavor threshold of below 500 ppm, areodorless or have high odor threshold, and/or are substantiallytransparent. In addition, or alternatively, the non-toxicliquid-impregnated surface for use with food products includes solids orimpregnating liquid that are tasteless and/or immiscible with anadjacent phase.

In some embodiments, the non-toxic liquid-impregnated surface can bedisposed on a substrate, for the example, the interior side wall of acontainer configured to house a drug or products classified as a drug,for example, an FDA approved drug for consumption by a human or ananimal. The drug can be in the form of a liquid, a cream, an ointment, alotion, an eye drop, an oral drug, an intravenous drug, an intramusculardrug, a suspension, a colloid, or any other form and can include anydrug included within the FDA's database of approved drugs. In suchembodiments, the materials included in the non-toxic liquid-impregnatedsurface can include an FDA approved drug ingredient, for example anyingredient included in the FDA's database of approved drugs,“http://www.accessdata.fda.gov/scripts/cder/drugsatfda/index.cfm.” theentire contents of which are hereby incorporated herein by reference. Insome embodiments, the non-toxic liquid-impregnated surface can includematerials that satisfy FDA requirements to be used in drugs or arelisted within the FDA's National Drug Discovery Code Directory,“http://www.accessdata.fda.gov/scripts/cder/ndc/default.cfm”, the entirecontents of which are hereby incorporated herein by reference. In someembodiments, the materials can include inactive drug ingredient of anapproved drug product as listed within FDA's database,“http://www.accessdata.fda.gov.scripts/cder/ndc/default.cfm”, the entirecontents of which are hereby incorporated herein by reference. In someembodiments, the materials can include any materials that satisfy therequirement of materials that can be used in liquid-impregnated surfacesconfigured to be used with food products, and/or include a dietarysupplement or ingredient of a dietary supplement.

In some embodiments, the non-toxic liquid-impregnated surface can bedisposed on a substrate, for the example, the interior side wall of acontainer configured to house a health and beauty product which is alsoclassified as a drug. Examples of such product can include, but are notlimited to toothpaste, sun screens, anti-perspirants, anti-dandruffshampoos, anti-dandruff conditioners, or anti-bacterial cleansers. Insuch embodiments, the health and beauty product, for example, toothpastecan include an impregnating liquid and/or a solid which is FDA approvedand satisfies FDA drug requirements as are listed within the FDA'sNational Drug Discovery Code Directory and can also include FDA approvedhealth and beauty ingredient, that satisfy FDA requirements to be usedin health and beauty products, satisfies FDA regulatory laws included inthe Federal Food, Drug and Cosmetic Act (FD&C Act), or the FairPackaging and Labeling Act (FPLA).

In some embodiments, the non-toxic liquid-impregnated surface can bedisposed on a substrate, for the example, the interior side wall of acontainer configured to house a health and beauty product, which doesnot include a compound classified by FDA as a drug compound or an activeingredient of a drug. Such products can include product configured tocontact the oral mucosa, for example non-fluoride toothpaste, some mouthwashes, mouth creams, denture fixing compounds, or any other oralhygiene product. In some embodiments, the health and beauty product caninclude a products configured for topical application, for examplecosmetics, lotions, shampoo, conditioner, moisturizers, face washes,hair-gels, medical fluids (e.g., anti-bacterial ointments or creams),any other health or beauty product, and or combination thereof. In suchembodiments, the non-toxic liquid impregnated coating can include, forexample, a material that is an FDA approved health and beautyingredient, or that satisfies FDA requirements to be used in health andbeauty products, FDA regulatory laws included in the Federal Food, Drugand Cosmetic Act (FD&C Act), and/or the Fair Packaging and Labeling Act(FPLA). In some embodiments, the solids and or impregnating liquidincluded in the non-toxic liquid-impregnated surface can include aflavor or a fragrance.

In some embodiments, the materials included in any of the non-toxicliquid-impregnated surfaces described herein (e.g., liquid-impregnatedsurfaces configured to contact food products, drugs, or health andbeauty products) can be flavorless or have high flavor thresholds below500 ppm, and can be odorless or have a high odor threshold. In someembodiments, the materials included in any of the non-toxic liquidimpregnating surfaces described herein can be substantially transparent.For example, the solid and the impregnating liquid can be selected sothat they have substantially the same or similar indices of refraction.By matching their indices of refraction, they may be optically matchedto reduce light scattering and improve light transmission. For example,by utilizing materials that have similar indices of refraction and havea clear, transparent property, a surface having substantiallytransparent characteristics can be formed. In some embodiments, thematerials included in the liquid-impregnated surfaces are organic or arederived from organically grown products.

In some embodiments, the liquid surface film includes a liquid having amelting point that is higher than the temperature at which the containerbearing said liquid surface film would typically be stored, shipped,transported, etc. In other words, the liquid may be frozen duringcertain such periods. When the liquid surface film is solidified throughfreezing, it dissolves much more slowly (e.g., in the presence of anadjacent product), and to a lesser extent, thereby enhancing thelifetime of the liquid surface film during storage. Upon thawing, theliquid surface film regains the performance characteristics that it hadprior to freezing (i.e., its “slippery” properties). This ability tofreeze the liquid component of the liquid surface film may be desirable,for example, during periods of time when the liquid surface film hasbeen applied to a container but the container does not yet contain aproduct, or when a product within a container coated with the liquidsurface film does not yet need to be dispensed (e.g., during shipment orstorage).

In some embodiments, the materials included in any of the non-toxicliquid-impregnated surfaces described herein can be recyclable. Forexample, the solid or impregnating liquid can include materials thatwash away during standard container (e.g., glass bottle, plastic bottle,etc.) recycling process. For example, the liquid-impregnated surface canbe configured to pass standard recycling tests provided by theAssociation for Postconsumer Plastic Recyclers (e.g., may be adequatelycleaned using the typical wash used in PET bottle recycling). In someembodiments, the liquid-impregnated surface can be configured todissolve in a caustic wash, for example a solution of Triton X 100 orNaOH at high temperature, an acid wash, a solvent wash, or any otherdissolving solution.

In some embodiments, the impregnating liquid included in the non-toxicliquid-impregnated surface can include one or more additives. Theadditive can be configured, for example, to reduce the viscosity, vaporpressure, or solubility of the impregnating liquid. In some embodiments,the additive can be configured to increase the chemical stability of theliquid-impregnated surface. For example, the additive can be ananti-oxidant configured to inhibit oxidation of the liquid-impregnatedsurface. In some embodiments, the additive can be added to reduce orincrease the freezing point of the liquid. In some embodiments, theadditive can be configured to reduce the diffusivity of oxygen or CO₂through the liquid-impregnated surface or enable the liquid-impregnatedsurface to absorb more ultra violet (UV) light, for example protect theproduct (e.g., any of the products described herein), disposed within acontainer on which the non-toxic liquid-impregnated surface is disposed.In some embodiments, the additive can be configured to provide anintentional odor, for example a fragrance (e.g., smell of flowers,fruits, plants, freshness, scents, etc.). In some embodiments, theadditive can be configured to provide color to the liquid-impregnatedsurface and can include, for example a dye, or an FDA approved coloradditive. In some embodiments, the non-toxic liquid-impregnated surfaceincludes an additive that can be released into the product, for example,a flavor or a preservative.

In some embodiments, the materials included in any of the non-toxicliquid-impregnated surfaces described herein can be organic or derivedfrom organically grown products. For example, the impregnating liquidscan include organic liquids that are often or sometimes non-toxic. Suchnon-toxic organic liquids can, for example, include materials that fallwithin the following classes: lipids, vegetable oils (e.g., olive oil,light olive oil, corn oil, soybean oil, rapeseed oil, linseed oil,grapeseed oil, flaxseed oil, peanut oil, safflower oil, palm oil,coconut oil, or sunflower oil), fats, fatty acids, derivatives ofvegetable oils or fatty acids, esters, terpenes, monoglycerides,diglycerides, triglycerides, mixtures of triglycerides such as MCT oil(medium chain triglyceride oil), triacetin, tripropionin, alcohols, andfatty acid alcohols. Examples of vegetable oils, suitable for use asimpregnating liquids in the non-toxic liquid impregnated surface of thepresent disclosure, are described in Gunstone, F., “Vegetable Oils inFood Technology Composition, Properties and Uses: 2^(nd) Ed.,” Wiley,John and Sons Inc., Pub. May 2011, the contents of which are herebyincorporated by reference herein in their entirety.

In some embodiments, any of the non-toxic liquid-impregnated surfacesdescribed herein can include organic solids, semi-solids, and/or liquidsthat are non-toxic and that fall within the following classes: lipids,waxes, fats, fibers, cellulose, derivatives of vegetable oils, esters(such as esters of fatty acids), terpenes, monoglycerides, diglycerides,triglycerides, alcohols, triacetin, tripropionin, citric triglycerides,propylene glycol, poly ethylene glycol, fatty acid alcohols, ketones,aldehydes, proteins, sugars, salts, minerals, vitamins, carbonate,ceramic materials, alkanes, alkenes, alkynes, acyl halides, carbonates,carboxylates, carboxylic acids, methoxies, hydroperoxides, peroxides,ethers, hemiacetals, hemiaketals, acetals, ketals, orthoesters,orthocarbonate esters, phospholipids, lecithins, any other organicmaterial or any combination thereof. Some examples of food-safeimpregnating liquids are medium chain triglyceride (MCT) oil, ethyloleate, methyl laurate, propylene glycol, propylene glycoldicaprylate/dicaprate, or vegetable oil, glycerine, and squalene. Insome embodiments, any of the non-toxic liquid-impregnated surfaces caninclude inorganic materials, for example ceramics, metals, metal oxides,silica, glass, plastics, any other inorganic material or combinationthereof. In some embodiments, any of the non-toxic liquid-impregnatedsurfaces described herein can include, for example preservatives,sweeteners, color additives, flavors, spices, flavor enhancers, fatreplacers, and components of formulations used to replace fats,nutrients, emulsifiers, surfactants, bulking agents, cleansing agents,depilatories, stabilizers, emulsion stabilizers, thickeners, flavor orfragrance, an ingredient of a flavor or fragrance, binders, texturizers,humectants, pH control agents, acidulants, leavening agents, anti-cakingagents, anti-dandruff agents, anti-microbial agents, anti-perspirants,anti-seborrheic agents, astringents, bleaching agents, denaturants,depilatories, emollients, foaming agents, hair conditioning agents, hairfixing agents, hair waving agents, absorbents, anti-corrosive agents,anti-foaming agents, anti-oxidants, anti-plaque agents, anti-staticagents, binding agents, buffering agents, chelating agents, cosmeticcolorants, deodorants, detangling agents, emulsifying agents, filmformers, foam boosting agents, gel forming agents, hair dyeing agents,hair straightening agents, keratolytics, moisturizing agents, oral careagents, pearlescent agents, plasticizers, refatting agents, skinconditioning agents, smooting agents, soothing agents, tonics, and/or UVfilters.

In some embodiments, the non-toxic liquid-impregnated surface caninclude non-toxic materials having an average molecular weight in therange of about 100 g/mol to about 600 g/mol. which are included in theSpringer Material Landolt-Bornstein database located at,“http://www.springermaterials.com/docs/index.html,” or in the MatNavidatabase located at “www.mits.nims.go.jp/index_en.html.” In someembodiments, the liquids have boiling points greater than 150° C., forexample 250° C. or below about 270° C., such that they are notclassified as volatile organic compounds (VOC's). In some embodiments, aliquid-impregnated surface can include an impregnating liquid whosedensity is substantially equal to the density of the product. Forexample, the ratio of impregnating liquid density to product density maybe in a range from 0.95:1 to 0.95:1.1. In some embodiments, the densityof the impregnating liquid may be about 1 g/cm³.

In some embodiments the liquid can include materials safe for skincontact or one that is a ingredient in a health and beauty product.Examples include silicone oils, fluorinated hydrocarbons, fluorinatedperfluoropolyethers, fluorinated silicones, aryl silicones, phenyltrimethicone, cyclomethicones, aryl cyclomethicones and hydrocarbonliquids including mineral oil, paraffin oil, C13-C14 isoparaffins,C16-C18 isoparaffins, di- and triglycyceride esters, tri alkyl esters ofcitric acid.

In some embodiments the solid material can include materials safe forskin contact or one that is a ingredient in a health and beauty product.Examples include the categories of silicones, alkyl silicone waxes,hydrocarbon waxes, polymethylsilsesquioxane particles, silica particleswith hydrophobic treatment (for example a hydrophobic silane), silicaparticles with polydimethyl siloxane (PDMS) resin outer layer,polymethylsilscsquioxane particles with polydimethylsiloxane resin outerlayer, silicone prepolymer mixes with combinations of silica and PDMSparticles, UV curable PDMS.

In some embodiments it is desirable for the textured solid and theimpregnating liquid to have substantially similar chemistry, such thatthe liquid has a high affinity for the solid and preferentially wet itbeneath a product. For example the solid could be PDMS and/or asiliconyl wax, and the liquid could be a silicone oil or dimethicone.These classes of materials are found to be effective combinations forcoatings for many consumer products including many hair gels,conditioner, and oil in water lotions. Another effective combination arewaxes that are food additives used as a solid that are impregnated witha liquid having substantially similar chemistry. For example, the solidcould be a triglyceride based wax and the liquid could be atriglyceride.

Creating a Matrix of Solid Features on an Interior Surface of a Bottle:

In these experiments, 200-proof pure ethanol (KOPTEC), powdered carnaubawax (McMaster-Carr) and aerosol carnauba wax spray (PPE, #CW-165, whichcontains trichloroethylene, propane and carnauba wax) were used. Thesonicator was from Branson, Model 2510. The advanced hot plate stirrerwas from VWR, Model 97042-642. The airbrush was from Badger Air-BrushCo., Model Badger 150.

A first surface having a matrix of solid features was prepared byProcedure 1, described as follows. A mixture was made by heating about40 mL of ethanol to a temperature of about 85° C., slowly adding about0.4 grams of carnauba wax powder, boiling the mixture for approximately5 min, and then allowing the mixture to cool while being sonicated forabout 5 min. The resulting mixture was sprayed onto a substrate with theairbrush (at an airbrush pressure of about 50 psi), and then allowed todry at ambient temperature and humidity for about 1 min. SEM images ofthe resulting surface are shown in FIGS. 12 and 13 (at 500× and 15,000×magnification, respectively).

A second surface was prepared by Procedure 2, described as follows. Amixture was made by adding about 4 grams of powdered carnauba wax toabout 40 mL ethanol and vigorously stirring. The resulting mixture wassprayed onto a substrate with the airbrush (at an airbrush pressure ofabout 50 psi) for about 2 seconds at a distance of about 4 inches fromthe surface, and then allowed to dry at ambient temperature and humidityfor about 1 min. SEM images are shown in FIGS. 14 and 15 (at 500× and15,000× magnification, respectively).

A third surface was prepared by Procedure 3, described as follows. Anaerosol wax was sprayed onto a substrate at a distance of about 10inches for about 3 seconds. The spray nozzle was moved such that sprayresidence time was no longer than about 0.5 sec/unit area, and then thesubstrate was allowed to dry at ambient temperature and humidity forabout 1 min. SEM images are shown in FIGS. 16 and 17 (at 500× and15,000× magnification, respectively).

Impregnating a Wax Coating:

A quantity of about 5 to about 10 mL of ethyl oleate (sigma Aldrich) orvegetable oil was swirled around in bottles that initially had aninternal surface entirely covered with wax (prepared by Procedure 3 asdescribed above), until the bottles became transparent. Such a coatingtime was chosen so that a cloudy (not patchy) coating formed over thewhole internal surface. The formed coating had a thickness in a range ofabout 10 microns to about 50 microns.

The excess oil was removed by inverting the bottles (i.e., holding themupside down) for about 5 minutes, or drained by adding about 50 mL ofwater to the bottle and shaking it for 5-10 seconds to entrain most ofthe excess oil into the water. The water/oil emulsion was then dumpedout. In general, after draining, the coating appears clear. When it isover-drained, however, it usually appears cloudy.

FIGS. 18 through 23 show time-lapse images of a volume of ketchup on aliquid-impregnated surface, prepared in accordance with an embodiment ofthe invention. As shown, the spot of ketchup was able to slide along theliquid-impregnated surface due to a slight tilting (e.g., about 5 toabout 10 degrees) of the surface. The ketchup moved along the surface asa substantially rigid body, without leaving any ketchup residue alongits path. The elapsed time from FIG. 18 to FIG. 23 was about 1 second.

Freezing a Liquid Impregnated Surface

A liquid-impregnated surface which included carnauba wax mixedtrichloroethylene as the solid, was impregnated with methyl laurate,which has a freezing point of 5° C. One PET bottle was coated withcarnauba wax impregnated with methyl laurate, and another one was coatedwith carnauba wax impregnated with ethyl oleate, which has a freezingpoint of −32° C. Both PET bottles were filled with scrambled egg yolk,and showed nearly identical slipperiness at room temperature, based onthe sliding speed of about 3 scrambled egg yolks at a 15° angle. Bothbottles were then placed in a freezer at −15° C. for 3 days, and uponthawing, the bottle having the liquid-impregnated surface that includedmethyl laurate showed no detectable change in performance, whereas theliquid-impregnated surface that included ethyl oleate exhibitedsignificantly lower sliding speed.

While various embodiments of the system, methods, and apparatuses of thepresent disclosure have been described above, it should be understoodthat they have been presented by way of example only, and are notlimited to the example set forth herein. Where methods and stepsdescribed above indicate certain events occurring in a certain order,those of ordinary skill in the art having the benefit of this disclosurewould recognize that the ordering of certain steps may be modified, andsuch modifications are therefore contemplated by this disclosure.Additionally, certain steps described herein may be performedconcurrently, e.g., in a parallel process, when possible, as well asperformed sequentially as described above. The embodiments have beenparticularly shown and described, but it will be understood that variouschanges in form and details may be made.

1. An apparatus comprising: a container including at least one interiorsurface, the at least one interior surface having: an arrangement ofsolid and/or semi-solid features thereon, the features defining one ormore regions therebetween; and an impregnating liquid preferentiallywetted to the one or more regions, and a consumable product containedwithin the container, the features and the impregnating liquidcollectively defining a secondary surface, wherein at least one of thefeatures and the impregnating liquid comprises a non-toxic material. 2.The apparatus according to claim 1, wherein the features comprise atleast one of: a lipid, a wax, a fat, a fiber, cellulose, a derivative ofa vegetable oil, an ester, a terpene, a monoglyceride, a diglyceride, atriglyceride, an alcohol, a fatty acid alcohol, a ketone, an aldehyde, aprotein, a sugar, a salt, a mineral, a vitamin, a carbonate, a ceramicmaterial, an alkane, an alkene, an alkyne, a carboxylates, a carboxylicacid, a methoxy, a hydroperoxide, a peroxide, an ether, a hemiacetal, ahemiaketal, an acetal, a ketals, a phospholipids, and a lecithin.
 3. Theapparatus according to claim 1, wherein the impregnating liquidcomprises at least one of: a triglyceride, glycol dicaprylate, propyleneglycol dicaprate, a vegetable oil, glycerine, propylene glycol, ethyl,and squalene.
 4. The apparatus according to claim 1, wherein theimpregnating liquid comprises at least one of: a lipid, a vegetable oil,a fat, a fatty acid, a derivative of vegetable oil, a derivative of afatty acid, an ester, a terpene, a monoglyceride, a diglyceride, atriglyceride, an alcohol, and a fatty acid alcohol.
 5. The apparatusaccording to claim 1, configured such that the secondary surfaceexhibits a roll-off angle for a 5 μL droplet of water of less than 10°.6. The apparatus according to claim 1, wherein the secondary surfacecomprises at least one of a surfactant, a flavorant, an antioxidant, ora dye.
 7. The apparatus according to claim 1, wherein the impregnatingliquid does not comprise a volatile organic compound (VOC).
 8. Theapparatus according to claim 1, wherein the at least one of the featuresand the impregnating liquid comprising a non-toxic material has amolecular weight of between about 100 g/mol and about 600 g/mol.
 9. Theapparatus according to claim 1, wherein at least one of the features andthe impregnating liquid is recyclable.
 10. The apparatus according toclaim 1, wherein at least a portion of the secondary surface isconfigured such that the impregnating liquid cloaks at least a portionof the consumable product.
 11. The apparatus according to claim 10,wherein a first portion of the secondary surface is configured such thatthe impregnating liquid wetted therein cloaks at least a portion of theconsumable product, and a second portion of the secondary surface isconfigured such that the impregnating liquid wetted therein does notcloak the consumable product.
 12. An apparatus comprising: a containerincluding at least one interior surface, the at least one interiorsurface having: an arrangement of solid features thereon, the solidfeatures defining one or more regions therebetween; and an impregnatingliquid retained, by capillary force, within the one or more regions, anda consumable product contained within the container, wherein at leastone of the solid features or the impregnating liquid comprises anon-toxic material.
 13. An apparatus comprising: a container includingat least one interior surface, the at least one interior surface having:an arrangement of solid and/or semi-solid features thereon, the solidfeatures defining one or more regions therebetween; and an impregnatingliquid disposed in the one or more regions, and a product containedwithin the container, wherein: (a) the impregnating liquid is siliconeoil, and the features exhibit a first characteristic length scale; or(b) the impregnating liquid is (BMIm), and the features exhibit a firstcharacteristic length scale, the features comprising secondary featureshaving a second characteristic length scale that is smaller than thefirst characteristic length scale.